Both. I really can't make up my mind when there are single player games like Deus Ex and System Shock 2, and multiplayer games like Counter-strike, warcraft 3 and Unreal Tournament.
I really enjoy the stories in good games like System Shock 2...it's like playing a movie. However I also really enjoy fragging some people, especially if they think that they are l33t.
Playing against computer controlled enemies gets a bit repetitive and predictable, even in UT /w godlike bots. That's why playing against other people is fun.